ABSTRACT:The problem of observation of continuous-time nonlinear Lipschitz systems under time-varying discrete measurements is studied. This class of systems naturally occurs when continuous processes are observed through digital sensors and information is sent via a network to a computer for state estimation. Since network introduces uncertainties in the sampling time, the observer must be designed so to take these uncertainties into account. Here two classes of observation scheme are studied. First an impulsive observers, which make instantaneous correction when information is received, is considered. Then a Luenberger-like observer with a piece wise constant correction term is studied. For both classes of observer, generic conditions are provided. Then a restriction of the generic conditions is used to establish tractable conditions that allows the synthesis of an observer gain.

BIOGRAPHY: Lucien Etienne received a M.Sc. Degree in applied mathematics at the INSA Rouen in 2012 and a joint Ph.D. in automatic control from the university of L'Aquila and the university of Cergy-Pontoise in 2016. After a Post-doc at INRIA Lille on observer synthesis for sampled data system, he is currently Post-doc at L2S Central Supéléc working on switched systems for embedded control under mixed stochastic/deterministic timing uncertainty.
His research interests include switched and hybrid systems, Observer synthesis and sampled data systems.

11h-12h: Wei Li (Nanjing University, China) - Cooperative Control of Multi-Agents: On a Sphere Manifold and in the Euclidean Space.

ABSTRACT: The talk will discuss cooperative control of multi-agents on a sphere and in the Euclidean space. We will first consider the control law design of agents on a sphere, and analyze the stability, scaling, and geometry properties, and discuss future directions. Then, for agents evolving in the Euclidean space, we will consider coupled agents with second-order dynamics. The state of a single agent includes both position and velocity, thus generally, the agents have both velocity coupling and position couplings (VCPC); and if we consider different VCPC, then interesting yet difficult problems arise. We then discuss two aspects of analysis on consensus convergence , and future directions.

BIOGRAPHY: Wei Li received the Ph.D. degree in Automatic Control from Shanghai Jiao Tong University, Shanghai, China, in 2008. From 2009 to 2010, he was a Post-Doctoral Research Associate with the Department of Electrical Engineering, The University of Texas at Dallas, Dallas, TX, USA. Since 2010, he has been an Associate Professor with the Department of Control and Systems Engineering, Nanjing University, Nanjing, China. His current research interests include robotics, autonomous mobile robots, decentralized control, cooperative control of mobile robotic agents, and wireless sensor networks. Dr. Li is an Associate Editor of Asian Journal of Control. He is a Senior Member of IEEE.

10H00-11H00 Nathan van de Wouw (Eindhoven University of Technology): The convergence property: system theoretic aspects and applications

ABSTRACT: In this talk, the convergence property, which is a system-level stability property of nonlinear dynamical systems originally introduced in the 1960's in Russia, will be discussed in detail. A convergent system exhibits a unique, bounded globally asymptotically steady-state solution. Lyapunov characterisations of sufficient conditions for and properties of convergent systems will be presented. Moreover, relations to notions such as e.g. incremental stability will be briefly addressed. In the second part of the talk it will be advocated that convergence is a useful property in the analysis and design of nonlinear control systems. Particular applications are: steady-state performance analysis through "nonlinear frequency response functions", output regulation (with tracking, synchronisation as particular sub-problems), observer design, model reduction and extremum seeking control.

BIOGRAPHY: Nathan van de Wouw (born, 1970) obtained his M.Sc.-degree (with honours) and Ph.D.-degree in Mechanical Engineering from the Eindhoven University of Technology, Eindhoven, the Netherlands, in 1994 and 1999, respectively. From 1999 until 2015 he has been affiliated with the Department of Mechanical Engineering of the Eindhoven University of Technology as an assistant/associate professor. Nathan van de Wouw currently holds an adjunct full professor position at the University of Minnesota, U.S.A and a (part-time) full professor position at the Delft University of Technology, the Netherlands. In 2000, Nathan van de Wouw has been working at Philips Applied Technologies, Eindhoven, The Netherlands, and, in 2001, he has been working at the Netherlands Organisation for Applied Scientific Research (TNO), Delft, The Netherlands. He has held positions as a visiting professor at the University of California Santa Barbara, U.S.A., in 2006/2007, at the University of Melbourne, Australia, in 2009/2010 and at the University of Minnesota, U.S.A., in 2012 and 2013. He has published a large number of journal and conference papers and the books 'Uniform Output Regulation of Nonlinear Systems: A convergent Dynamics Approach' with A.V. Pavlov and H. Nijmeijer (Birkhauser, 2005) and `Stability and Convergence of Mechanical Systems with Unilateral Constraints' with R.I. Leine (Springer-Verlag, 2008). He currently is an Associate Editor for the journals "Automatica" and "IEEE Transactions on Control Systems Technology". His current research interests are the analysis and control of nonlinear/hybrid systems, with applications to vehicular platooning, high-tech systems, resource exploration and networked control systems.

ABSTRACT: Model reduction is a tool for the approximation of complex dynamical systems by systems of reduced order, hereby enabling efficient analysis or controller synthesis. In this presentation, several methods for model reduction of nonlinear systems will be discussed. These methods have in common that they rely on incremental system properties in obtaining an accurate reduced-order model that preserves relevant stability properties and satisfies an a priori bound on the reduction error. Specifically, (input-to-state) convergent nonlinear systems will be considered, in which reduction is performed by isolating the nonlinearities and the application of linear model reduction techniques. Next, the reduction technique of incremental balanced truncation is introduced, which explicitly takes nonlinearities into account in the reduction procedure and can be regarded as an extension of the well-known technique of balanced truncation to the nonlinear domain.

BIOGRAPHY: Bart Besselink is a Postdoctoral Researcher with the ACCESS Linnaeus Centre and Department of Automatic Control at KTH Royal Institute of Technology, Stockholm, Sweden. He received the M.Sc. degree (cum laude) in Mechanical Engineering from Eindhoven University of Technology, Eindhoven, the Netherlands, in 2008. In 2012, he received the Ph.D. degree from the same university for his thesis on model reduction techniques for nonlinear control systems. He was a short-term Visiting Researcher at the Tokyo Institute of Technology, Tokyo, Japan, in 2012. His main research interest include systems theory and model reduction for nonlinear dynamical systems and large-scale interconnected systems. In addition, he is working on applications in the field of intelligent transportation systems with a particular focus on the control and coordination of heavy-duty vehicle platoons.

Résumé de Daniel Han Kwan:
The Vlasov-Poisson system is a classical PDE model of plasma physics, used to describe the dynamics in phase space of interacting charged particles. We will review some remarkable mathematical properties of this system. The topics reviewed should include (1) the existence of weak or strong solutions, (2) the stability and instability theory of certain equilibria, (3) the quasineutral limit, i.e. the regime when the Debye length is small compared to the typical observation length.

Programme :- 9h30-10h00 Accueil (café)- 10h00 - 11h00 Corentin Briat (ETH Zürich) : Convex conditions for stability analysis and stabilization of linear aperiodic impulsive systems with applications to asynchronous sampled-data systems
This talk is about the analysis and control of linear impulsive systems using clock-dependent Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to the stability of aperiodic systems under minimum, maximum and ranged dwell-times are then derived. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of state-feedback controllers, providing then a convex solution to the (previously open) problem of dwell-time stabilization of impulsive systems using hybrid stability criteria. By finally relying on the representability of sampled-data systems as impulsive systems, the problem of robust stabilization of periodic and aperiodic uncertain sampled-data systems is straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach.

- 11h00 - 12h00 Antoine Girard (CNRS, L2S): Reachability analysis of linear hybrid systems - application to stability analysis of linear aperiodic impulsive systems.
In the first part of this talk, I will present the basics of computational reachability analysis for hybrid systems. I will then focus on the presentation of scalable and accurate algorithms for reachability analysis of linear systems. In the second part of the talk, I will show how these algorithms can serve for stability analysis of a class of linear aperiodic impulsive systems. Applications of our approach to verification and synthesis of timing contracts for implementation of embedded controllers will conclude the talk.

Résumé de N. Spillane : domain decomposition methods are a family of solvers tailored to very large linear systems that require parallel computers. They proceed by splitting the computational domain into subdomains and then approximating the inverse of the original problem with local inverses coming from the subdomains. I will present some classical domain decomposition methods and show that for realistic simulations (with heterogeneous materials for instance) convergence usually becomes very slow. Then I will explain how this can be fixed by injecting more information into the solver, either by adding a coarse space (this is also known as deflation) or by using multiple search directions within the conjugate gradient algorithm.

Résumé de S. Molchanov : the fractal lattice Γ is a skeleton, i.e. the discrete approximations of the nested fractal, say, the infinite Sierpinski gasket. The dimension d (Γ) of such lattice (Hausdorff’s dimension or spectral dimension) can be different but in all cases it has values on the interval (1,2).The Anderson Hamiltonian has the standard definition : Δ is the lattice Laplacian, (X_i) are i.i.d. random variables and σ is a coupling constant. We will discuss the following recent results :
a) The spectrum of H has no a.c. component P-a.s. for any non-degenerated potential.
b) If the random variables are heavy tailed, then the spectrum of H is p.p. P-a.s. This fact must be true for the arbitrary random variable, but it has not been proved.
Several results for the deterministic potential will be also presented.

Bio : John Skilling was awarded his PhD in radio astronomy in 1969. Through the 1970s and 1980s he was a lecturer in applied mathematics at Cambridge University, specialising in data analysis. He left to concentrate on consultancy work, originally using maximum entropy methods but moving to Bayesian methodology when algorithms became sufficiently powerful. John has been a prominent contributor to the “MaxEnt” conferences since their beginning in 1981. He is the discoverer of the nested sampling algorithm which performs integration over spaces of arbitrary dimension, which is the basic operation dictated by the sum rule of Bayesian calculus.

I/ The application of medium grazing angle sea-clutter modelsThere is a large body of literature on sea-­clutter analysis and modelling. However, these are mostly from radars with coarse resolution with data collected at low grazing angles. Newer maritime airborne radars which operate at higher resolutions and from higher grazing angles will therefore require newer models to characterise this sea clutter.... click here for know moreII / The NRL multi­‐aperture SAR : system description and recent resultsThe Naval Research Laboratory (NRL) multi-­‐aperture synthetic aperture radar (MSAR) is an airborne test bed designed to investigate remote sensing and surveillance applications that exploit multiple along-­‐track phase centers, in particular, applications that require measurement of scene motion....click here for know more

Bio : Luke Rosenberg received his Bachelor of Electrical and Electronic Engineering in 1999, Masters in Signal and Information Processing in 2001 and PhD in 2006 all from the University of Adelaide in Australia. In 2000 he joined the Defence Science and Technology Organisation as an RF engineer, then worked as a research scientist in the imaging radar systems group and recently in the maritime radar group. He is also an adjunct senior lecturer at the University of Adelaide and is currently on attachment at the US Naval Research Laboratory working on algorithms for focussing moving scatterers in synthetic aperture radar imagery.

Abstract : The main objective of the field of Computational Neuroscience is to understand how the brain works through mathematical models (numerical and analytical works). Some of these models are described by neural fields equations. Neural fields are integro-differential equations that describe the spatiotemporal dynamics of the activity of a piece of neocortical tissue. Neural fields equations emerge when one assimilates the high number of neurons of the selected piece of brain tissue in its continuum limit. Neural fields have been studied both analytically and numerically by many researchers. They can model many different and interesting biological phenomena such as attention, working memory, self-organization, or synaptic depression. The seminar consists of two parts. The first part is a brief introduction to neuroscience and the second part is dedicated to neural fields. We will review how neural fields equations can be derived, how the steady-state solution can be computed, and its stability can be insured. Finally, some cognitive models that are based on neural fields will be presented.

Bio : Georgios Detorakis has studied Applied Mathematics and Neuroscience. He did his PhD on cortical plasticity, self-organization and neural fields. During his PhD, he studied the formation of topographic maps in area 3b of the primary somatosensory cortex and the multimodal problem of “Touch and the body”. He is now a postdoc fellow at L2S working with Antoine Chaillet on Parkinson’s disease in the ANR project "SynchNeuro". He uses delayed neural fields in order to model some brain areas that play a crucial role in Parkinson’s disease motor symptoms.

10H30-11H30 Manfredi Maggiore, University of TorontoTitle : an Introduction to Virtual Holonomic Constraints

Abstract : in Lagrangian mechanics, constraints that can be expressed in the form of equations involving only configuration variables, and not their derivatives, are called "holonomic." For example, a particle constrained to move on the surface of a sphere is subject to a holonomic constraint. In the case of Lagrangian control systems, one may use feedback to emulate the presence of holonomic constraints. For example, one may make a platoon of vehicles move in rigid formation by emulating the presence of distance constraints among the vehicles. Such emulated constraints are called "virtual holonomic constraints" (VHCs). In robotics, VHCs have become a popular tool to induce stable walking gaits in biped robots, and there is a growing body of work suggesting that VHCs might represent a universal paradigm for locomotion. From a theoretical viewpoint, there are a number of interesting questions arising in the context of VHCs. One of them is whether or not the motion of a Lagrangian control system subjected to a VHC is still Lagrangian. In this second talk I will show that, in contrast with classical mechanics, the answer to this question is "typically no." For underactuated Lagrangian control systems with underactuation degree one, I will give necessary and sufficient conditions guaranteeing that the constrained dynamics arising from a VHC are Lagrangian. I will show experimental results illustrating VHCs in action and giving an intuitive feel of the significance of Lagrangian constrained dynamics.

Bio : Manfredi Maggiore is currently visiting L2S on sabbatical leave from the University of Toronto. Born in Genoa, Italy, he received the Laurea degree in Electrical Engineering in 1996 from the University of Genoa and the PhD degree in Electrical Engineering from the Ohio State University, USA, in 2000. Since 2000, he has been with the Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Canada, where he is currently Professor. He has been a Visiting Professor at the University of Roma Tor Vergata (2001) and the University of Bologna (2007-2008). His research focuses on mathematical nonlinear control, and relies on methods from dynamical systems theory and differential geometry.